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A Philosopher’s Experiment Teaching Math and the Arts (guest post by Yann Benétreau-Dupin)

Published by Anonymous (not verified) on Fri, 31/08/2018 - 1:04am in

The following is a guest post*  from Yann Benétreau-Dupin, a lecturer in philosophy at San Francisco State University, about an interesting and innovative response to the California State University system’s change to its general education requirements: a course on math and the arts, taught in the philosophy department.


[from “Theorica musicae” by Franchino Gaffurio]

A Philosopher’s Experiment Teaching Math and the Arts
by Yann Benétreau-Dupin

What if a philosophy department offered a math general education course for liberal arts students? This is the audacious idea the San Francisco State University (SFSU) Philosophy Department had after the California State University system decided to reform its general education math requirements. Among the changes are a push to diversify methods and contents, a more student-centered curriculum, as well as an end to demanding, for those who would need it, remedial courses prior to enrolling college-level courses. Instead, general education math courses are to be offered with additional support for those who are not “college ready” in math or stretched over two semesters.

It is in this context that SFSU Philosophy, with some input from music and art history faculty, decided to offer its own math course, titled “The Art(s) of Quantitative Reasoning.” Although I was part of the team that put together this proposal, this blog post only addresses the content, methods, and results of this course’s first iteration this past spring semester.

Last semester’s results are encouraging: it is possible for a philosophy department to offer an original non-remedial, general education math/quantitative reasoning course without prerequisite on content that non-majors will find more palatable than that offered in a traditional math course. Because this class’s content can be covered with minimal (high-school level) mathematics background knowledge, this can be viewed as an encouraging experiment in STEAM education in which philosophers can partake. Because the pedagogical approach was mostly problem-based and inquiry-based, with Socratic questioning instead of lecturing (or as a student called it, “going over all the wrong answers before getting the right one”), I am confident that this sort of courses can find a home in other Philosophy departments, albeit not without much preparation.

The approach chosen in my course was to focus on a few issues in quantitative reasoning that have shaped the history of the arts, that is, to study a few cases in the history of the arts that posed a technical—mathematical—problem and different ways to overcome this problem. The course’s two main units were the problem of musical tuning and temperament, and perspective and projective geometry in visual arts. The problem of tuning is that of a choosing a way to define a musical scale. As explained in this short video, it is impossible to design a musical scale with 12 semitones per octave (which is what we are used to) such that all four following criteria are met simultaneously:

  • all 12 semitones are equally spaced,
  • closeness: a method of partitioning the scale—e.g., of defining an interval of 7 semitones or 5 whole tones—will carry over several octaves (e.g., 12 intervals of 7 semitones will be equivalent to 7 octaves),
  • flexibility: a scale defined from a given note (e.g., C) will produce similar intervals whatever key we play in (i.e., if we took any other note as the fundamental note in our scale),
  • certain harmonious intervals between notes in the scale obtain (e.g., there are notes in the scale that are such that the ratio of their frequency with that of the fundamental is a simple one of, e.g., 3:2 or 4:3).

Given that I couldn’t assume that the students would be familiar enough with square roots, powers, or even how to add or multiply fractions, the video linked earlier summarizing the problem of tuning and temperament came at the end of several weeks of instruction as a way to recap all we had previously covered.

The pedagogical approach was mostly problem-based. A large number of class meetings revolved around problem sets to be solved individually or (preferably) in small groups: often the problems would allow for different solving methods or even answers, and the students were encouraged to justify and compare their method. Outside of class time, students weren’t assigned readings but rather problem sets (6 over the semester). For instance, for the perspective and projective geometry unit, students were assigned exercises from the first part of this problem set asking them to explain and apply Albrecht Dürer’s perspective method.


Albrecht Dürer, “Man Drawing a Lute”

The following table gives an overview of the syllabus:

Topics
Main notions
Other notions

Change ringing
Counting arrangements, finding patterns, proving generalizations (proof by induction)
The general, abstract notion of operation (whether addition or bell switch) abstractly and how group theory allows one to identify all possible patterns of (church) bell ringing

Pitches and notes
Defining intervals as ratios of frequencies; adding intervals corresponds to multiplying these ratios; frequency as the inverse of string length; some pitches that sound well with a fundamental of frequency f have frequency 2f, 3f, 4f, etc. Why there are 12 notes in our usual scale: dividing the scale equally in 12 allows us to approximate the well-sounding ratios 3:2 and 4:3 better than other numbers
The class of frequency any note of frequency f defines at different octaves: f*2^n, with n integer. Linear v. exponential growth (from one note to the next, frequencies grow exponentially); this allowed for connections with topics not related to the arts.

The Pythagorean scale
Pythagoras’s method: once a fundamental note of frequency f is chosen, all 12 semitones are of the form (3^m/2^n)*f, with m, n integers;
How this method doesn’t meet any of the four criteria for musical scales presented above

Other scales: Just intonation
This less flexible method favors simple ratios (e.g., it replaces the Pythagorean major third defined with the ratio 81:64 with the more harmonious-sounding ratio 5:4).

Other scales: equal temperament
Square roots and other roots. This flexible, close, and equally-spaced method is the one we now have to tune pianos.
This method has neither other scales’ well-sounding ratios nor the ability to render the out-of-tune major third used in Gothic music

Rules of perspective
Parallel lines, parallel lines in real life v. their projection on a plane; parallel lines not parallel to the picture plane have a vanishing point; Alberti’s method to draw a square-tiled floor
Alberti’s interpretation of Euclid’s axioms for perspective (vision occurs on a straight line, from a single point, etc.); identifying what rules of perspective Medieval paintings failed.

Beyond 1-point perspective
1-point, 2-point, and 3-point perspective; the role of a choice of perspective to create the impression of motion
In 2-point perspective, the distance between vanishing points depends on the viewing distance; drawing a checker in 2-point perspective

Projective geometry
Elements of perspective (plane, viewing point, etc.); elements of projection (center of projection, image, object) and different types of projection (camera obscura, shadow, etc.); how lines can intersect a plane, planes a plane, etc.
Desargues’s theorem applied to the drawing of shadows

Apart from problem sets and tests, students were asked to write a 1,400-word research paper discussing the interaction between math and the arts. The choice of topic was left open: a specific artist’s oeuvre or work of art, a problem covered in class or not, or a more philosophical issue, etc. Students had to present each other in their group their topic of choice over a week before turning in their paper. Pleasantly, few students chose my suggestions of topic and resources. The papers discussed Mondrian’s oeuvre; explained why a photographer has to balance aperture, sensibility, and shutter speed; examined the reasons behind the choice of 440Hz as the “concert A”; presented the basics of tessellation and how to construct a non-repetitive infinite tiling; answered the question of whether mathematical constraints foster or hinder creativity by comparing Western and Eastern musical scales.


Piet Mondrian, “Composition with Yellow, Blue and Red”

The main student learning objectives were those of the university’s math/quantitative reasoning requirement, e.g., to represent mathematical information symbolically, visually, numerically, and verbally; interpret mathematical models such as formulae, graphs, tables, and schematics, and draw inferences from them; estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results, etc. These are consistent with a common-core approach. The unit on perspective allowed for more practical, concrete activities (projecting parallel real buildings’ parallel lines onto a window, drawing shadows, identifying vanishing points, etc.) than other units.

With a manageable class size (capped enrollment), groups were formed freely and remained mostly constant throughout the semester, with the only constraint that they had to include students of different level of interest—not necessarily ability—in mathematics. Grading was done anonymously. In lieu of additional remedial courses, a teaching assistant (a Philosophy MA student with a background in music and music theory) held weekly office hours (in addition to my own office hours).

The obstacles to teaching such a course were many. It requires prior knowledge in music and the arts, certainly more knowledge than I had if I had wanted this course to be more student-centered, incorporate their own knowledge and interests, and offer more tangible activities and group projects. And in order to help instructors prepare, there is unfortunately little material appropriate to this level of instruction. Several textbooks on the connection between music and mathematics exist, but they either assume much more math background than was appropriate (e.g., Benson 2007 or Roberts 2016) or else contain very little formalism (e.g., Harkleroad 2006 or Isacoff 2009). And there isn’t much audio material about tuning; you can hear for yourself here which tuning method you prefer. More teaching material is available for perspective and projective geometry (e.g., Frantz & Crannell 2011 or Dillon 2014), but little that is intended to non-majors (Professor Crannel’s course materials for majors were very useful, but I had to simplify them for this course). Unlike the musical scale unit, I taught the perspective and projective geometry unit without having to write more than one or two equations.

The choice of curriculum presented above may seem ambitious for an intro-level math course that also, in fact, doubles as a remedial course. There was no time to engage in philosophical discussion, nor even to work on writing skills for the research paper nearly as much as I would have done in a regular philosophy class.

Now, such a course’s main objective was to address non-majors, liberal arts students and offer them an opportunity to strengthen or develop their mathematical skills around topics they would find more palatable than in a traditional math course. In order to assess this, I conducted a pre/post test with the sort of questions that would help determine whether a student is “college ready” in math or not. The pre and post assessments were very similar, and neither the result nor the content of the pre-test were discussed before students took the post-test. More importantly, most of this test’s content was not explicitly covered during the semester. The following graphs show that overall students’ elementary knowledge improved, but this was much more true of those whose initial knowledge was lower, to the point where pre- and post-test results are not correlated.

Assuming that any further analysis of the data is meaningful at all (given how small the sample size is), I found that these results depend on gender (women’s scores improved more than men’s), but not on year (e.g., no significant difference between freshmen and seniors).

* * * * * * *

Acknowledgments: Steven Gomez was teaching assistant in my class. SFSU faculty involved in the broader course project are Associate Dean Susan Shimanoff; Professor Anita Silvers, Caitlin Dolan, Professor Ásta, and Professor Justin Tiwald (Philosophy); Professor Gail Dawson (Art History); and Professor Cyrus Ginwala (Music). Additional support was provided by Professor Serkan Hosten and Professor Kim Seashore from the Math department. Special thanks to Dr. Rachel Devorah Wood Rome at Berklee, Professor Dillon, and Professor Roberts.

References

Benson, David J. Music: A mathematical offering. Cambridge University Press, 2007.
Dillon, Meighan. “Projective Geometry for All.” The College Mathematics Journal 45.3 (2014): 169-178.
Frantz, Marc, and Annalisa Crannell. Viewpoints: Mathematical perspective and fractal geometry in art. Princeton, NJ: Princeton University Press, 2011.
Isacoff, Stuart. Temperament: How music became a battleground for the great minds of Western civilization. Vintage, 2009.
Harkleroad, Leon (for the MAA). The math behind the music. Cambridge University Press, 2006.
Roberts, Gareth E. From music to mathematics: Exploring the connections. JHU Press, 2016.

The post A Philosopher’s Experiment Teaching Math and the Arts (guest post by Yann Benétreau-Dupin) appeared first on Daily Nous.

The Cell Phone and the Virgin: A Montreal Odyssey

Published by Anonymous (not verified) on Fri, 31/08/2018 - 1:00am in

Tags 

art, philosophy

Edward Curtin And the sun pours down like honey on our lady of the harbor And she shows you where to look among the garbage and the flowers There are heroes in the seaweed, there are children in the morning They are leaning out for love and they will lean that way forever While Suzanne holds her mirror” Leonard Cohen, “Suzanne” Before this historical chasm, a mind like that of Adams felt itself helpless; he turned from the Virgin to the Dynamo as though he were a Branly coherer. On one side, at the Louvre and at Chartres, as he knew by the record of work actually done and still before his eyes, was the highest energy ever known to man, the creator of four-fifths of his noblest art, exercising vastly more attraction over the human mind than all the steam-engines and dynamos ever dreamed of; and yet this energy was unknown to the American mind. An American Virgin would never dare command; an American Venus would never dare exist.” Henry Adams, “The Dynamo and …

The Melodramatic Side of Political Economy

Published by Anonymous (not verified) on Sat, 25/08/2018 - 11:14pm in

Miss Prism: “Cecily, you will read your Political Economy in my absence. The chapter on the fall of the Rupee you may omit. It is somewhat too sensational. Even these metallic problems have their melodramatic side.” Cecily [Picks up books and throws … Continue reading →

October 14 event with Zsuzsanna Budapest

Published by Anonymous (not verified) on Wed, 22/08/2018 - 10:41am in

I’ll be returning to my old stomping grounds of Santa Cruz, CA in October (actually part of a longer North American film festival tour with Seder-Masochism, which I’ll announce soon).

Animated poster! Please share.

Animated poster! Please share.

The Goddess Animated: Nina Paley and Zsuzsanna Budapest

Double feature of Nina Paley animation! Each screening followed by dialog with Zsuzsanna Budapest and question-and-answer with audience.

1pm: Sita Sings the Blues
2009 Dir. Nina Paley
Paley’s award-winning 2009 animated musical interpretation of the Hindu epic Ramayana has earned widespread critical praise, a 100% rating on RottenTomatoes, and continued places on best-of lists. Roger Ebert wrote of it, “I am enchanted. I am swept away. I am smiling from one end of the film to the other.”

4pm: Seder-Masochism
2018 Dir. Nina Paley
Loosely following a traditional Passover Seder, events from the Book of Exodus are retold by Moses, Aharon, the Angel of Death, Jesus, and the director’s own father. But there’s another side to this story: that of the Goddess, humankind’s original deity. Seder-Masochism resurrects the Great Mother in a tragic struggle against the forces of Patriarchy.

Suggested donation: $20 to support the Women’s Spirituality Forum.
Tickets at the door.

AMAZONS ENCOURAGED TO ATTEND!

Sunday October 14, 2018
Click image for high resolution poster to print out

Click image for high resolution poster to print out

Brookdale Terrace Club House
300 Plum St., Capitola, CA
Please carpool; parking is limited.

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Crowdsourced funding as a ‘basic income’ for artists

Published by Anonymous (not verified) on Fri, 17/08/2018 - 12:55pm in

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Op-ed, Opinion, art, Artists

What do we do when the future we want is precluded by precarious economic conditions or a staleness social system?

The post Crowdsourced funding as a ‘basic income’ for artists appeared first on BIEN.

An introduction to my blog, and notes on an anarchist approach to industrial art

Published by Anonymous (not verified) on Sun, 12/08/2018 - 7:02am in

image/jpeg icon500full-nuestro-culpable-screenshot.jpg

A short post detailing the ethos behind my blog, and an example of me attempting to apply this ethos to a practical problem: that of collective creative art.

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Museums behaving badly

Published by Anonymous (not verified) on Wed, 08/08/2018 - 10:01am in

Tags 

art, Education

I love museums. Science museums, history museums, art museums; there’s nothing like looking at real stuff in person. Whether it’s an antique automobile, a big old beetle in a case, or the Ardabil carpet in the V&A, being able to walk around it, get close, and engage on my own time is one of my top-level pleasures.  I’m sure I learned as much natural science in the American Museum of Natural History as a child as I did in school; whenever I’m traveling, I make a beeline for local museums.

The affection is not entirely requited in art museums, mainly  because so many of them transparently disrespect me (and all the other visitors) by pointless, insouciant, arrogant stinginess with the information that makes the art accessible.  This weekend I was at the Huntington, the Getty Villa, and LACMA in LA. The Huntington and the Getty do a pretty good job with long, informative labels that provide context, history, and some guidance about what to attend to in the works on display, but LACMA left me really steamed.

A featured exhibition was several galleries full of contemporary political art by Iranians that reached back to the Shahnameh for analogies and references, a show with appropriate local interest (there are lots of Persians in LA, including refugees from before and after the shah’s overthrow) and in any case an interesting and fruitful concept.   You should go and see it, but unfortunately you will miss a lot unless you’re already hip to recent (and ancient) Iranian history, and can read Farsi. The labels were tiny and short and one after another very political work full of incriptions, signs, and text in Farsi was untranslated. One faceplant in particular seemed to sum up art museums’ worst instincts to make not only the typical visitor, but almost any visitor, feel unqualified and inadequate.

The work, by Koushna Navabi, is a couple of dozen rings in different metallic finishes with the same portrait, a little over an inch each way:

This is the entire label we were offered:

Know whose portrait this is? Only because I’m old enough to almost remember the period, and spent some time in Iran after the coup that overthrew him, I recognized Mohammed Mosaddegh, about whom Wikipedia says “Many Iranians regard Mosaddegh as the leading champion of secular democracy and resistance to foreign domination in Iran’s modern history. Mosaddegh was removed from power in a coup on 19 August 1953, organised and carried out by the CIA at the request of MI6.” In  the oppressive regime of the shah and his SAVAK secret police that followed, Iran’s oil remained in the hands of western oil companies and their US and British protectors. Of course by 1979 this arrangement went off the rails because the Iranians had had enough of it.

Any of that useful in engaging with this work? Or is the (I presume) affectionate but rather obscure pun in the title all you needed? I hung around and asked at least a half-dozen visitors if they knew whose portrait was on the rings; none had any idea. Here’s what the curator thought she was doing with this show; I’m sure her middle-east specialist colleagues were impressed, but an exhibition like this is a lot of work: I guess she just didn’t have a minute to actually think about the visitors who would walk in the door.

New “Prehistoric Goddess/Female Figures” Quilts

Published by Anonymous (not verified) on Sun, 05/08/2018 - 6:46am in

When Enlightenment understands its own Violence

Published by Anonymous (not verified) on Wed, 25/07/2018 - 10:36pm in

Tags 

art, Politics

Lévi-Strauss claims that, for the isolated tribe with whom an anthropologist makes first contact -- the tribe who, after being studied, will be decimated by diseases to which they've no resistance, then (if they've survived) converted to Christianity and, eventually, conscripted into semi-bonded labour my mining and logging companies -- for them, civilization represents no less than a cataclysm. This cataclysm, he says, is the true face of our culture -- the one that's turned away, from us at least. The order and harmony of the West, the laboratory in which structures of untold complexity are being cooked up, demand the emission of masses of noxious by-products. What the anthropologist encounters when he ventures beyond civilization's perimeter-fence is no more than its effluvia, its toxic fallout. The first thing we see as we travel round the world is our own filth, thrown into mankind's face.--12.10 from Satin Island (2015) by Tom McCarthy (emphasis in original)

One way to understand the revival of the so-called populist, racialized nationalism today is for a keen wish to restore the appearance of "order and harmony of the West" and to keep the noxious by-products of civilization out of sight behind the "perimeter-fence." While the critics of such populism primarily see it as an immoral (because partial) and even violent project, the populist understands himself in moral terms, part of a process of national purification even if (as is sometimes ruefully acknowledged) the agents that facilitate this purification are (rather) imperfect.

Of course, the populist does not allow himself to acknowledge that what it despises and loathes is itself its own filth or the effects of colonial and ongoing political interventions by the West. And often he conflates his own nostalgia with a historical fiction of once steady order and harmony. 

What makes reading Satin Island so interesting is that it allows us to see that populist ideas are, in fact the shadow lives of the purportedly self-critical ideas of the contemporary intelligentsia reflected in a subtly distorted mirror. The novel presents us with a main protagonist, an anthropologist who works for a corporation. The corporation "uses the Future to confer the seal of truth on these scenarios and assertions, making them absolute and objective simply by placing them within this Future: that's how we won contracts." It does so with self-understanding: "Everything, as Peyman [the visionary CEO and networker of the Company] said, may be a fiction--but the Future is the biggest shaggy-dog story of all." (8.7) The satirical echoes of Hegel's secularization of Christianity and contemporary theories of reflexivity are undoubtedly intentional here.

What is notable about the quoted passage (12.10), is that it, in turn, reflects a violent delusion of those intellectuals who take themselves to be self-critical heirs of the Enlightenment.+ These intellectuals understand themselves as self-critical, as tracking the all--too-human-costs of civilization, as recognizing that the scientific enterprise itself may be complicit in the very violence of the West; who speak with moral superiority -- because they take pride in frankly acknowledging the violent facts, as if it shows moral fortitude to acknowledge the facts --  and who recognize their own complicity in a system founded on and maintained by violence. In this self-serving fantasy -- but like other fictions it can be made real -- , the modern intelligentsia are the meritocratic elites who understand themselves as cogs in the research and design centers of a hegemonic, world wide civilization characterized by 'complexity.'

Part of the pedantic point of the novel is to show the ever-present desire to perpetrate a gesture of violence against the system by the boys in the Research & Design centers, and simultaneously a kind of obtuseness on their part toward the very real (patriarchal) violence within the hegemonic order against those that merely wish to register their ritualized dissent from the status quo. The obtuseness is not an accident, but a feature.

Above, I suggested that the populist and the self-critical intellectual share an outlook. One commonality is that they both understand the 'West' as 'civilized' and fail to acknowledge the true barbarism within, violence (see 13:12), that makes possible purported 'order and harmony.' They (that is, the populist and the self-critical-intellectual) both treat 'Western' superiority as an unquestionable given. The populist justifies it because she sees the world in zero-sum terms, if 'we' don't project power 'they' will take advantage to us; the would-be self-critical intellectual, takes it as a regrettable given that, while requiring an originary acts of violence,  makes a win-win future possible. What the intellectual does not do is question the very idea of a West. 

Satin Island makes us feel the barbarism within without offering either a scenario or a new language for overcoming it. One may say, then, it disowns the very possibility of researching and designing a better product. This very disowning may be a necessary step on the path of a truer liberation or it may be a quietist gesture characteristic of the reactionary mind unwilling to forego the inherited comforts.

+There are, also, of course propagandists of the Enlightenment who do not acknowledge costs of Enlightenment; there is an insatiable demand for their products.

Two iconic portraits

Published by Anonymous (not verified) on Sun, 22/07/2018 - 2:00am in

Tags 

art, Religion

My reaction to Vermeer’s Girl with a Pearl Earring in the Mauritshuis museum in The Hague surprised me. I was expecting to admire this famous work by a great master, the favourite painting of the Dutch. It is indeed technically marvellous. Vermeer was one of the greatest technicians of oil painting ever. My problem with the picture is as a portrait. It’s formally a tronje, a painting of an unidentified and representative human figure. But it’s plainly not a stylised ideal but a portrait of a real girl. She has no name, perhaps (as in the film) a servant paid a few ducats to sit. I find it unflattering, and not by any lack of skill. Newspapers rightly get criticised for printing photos of politicians with their mouths open: everybody looks stupid when caught like this. Vermeer went to enormous trouble, over multiple sittings, to make his subject look dimwitted. She was exophthalmic anyway, and he faithfully reproduced or exaggerated this. The combined effect is disrespectful and exploitative. And to what purpose? Possibly to make a trite contrast with the perfection of the enormous pearl earring lent her for the occasion. Pshaw.

My second portrait is an extreme contrast: Nefertiti, Queen of Egypt for almost 20 years, in Berlin. Again, the extraordinary technical skill of the bust (about two-thirds life size) is indisputable. The effect is remarkable. She is not just beautiful but glamorous: beauty weaponized. (The origins of the word lie in Scottish witchcraft.) For what purpose? The classic glamour photos of Hollywood studio stars were designed to transform their exploited and vulnerable subjects into unattainable objects of sexual desire, in order to sell film tickets. Nefertiti didn’t need that; she was a Pharaoh’s queen already.

The Hollywood stars were metaphorical sex goddesses. Nefertiti was the real thing.

First, the sex part. There is no reason to doubt her depicted beauty. Her husband Amenhotep was portrayed as ugly, with distended belly and elongated limbs, possibly as a result of a congenital condition. So the burden of regal show, and quite likely of day-to-day rule, fell disproportionately on the queen. She rose to the challenge; she even had herself sculpted naked, a radical step in any culture that you can only get away with if you have a great body and total self-confidence.

Second, the goddess. Pharaohs and their consorts were semi-divine personages anyway, on speaking terms with the gods. But Amenhotep IV – Akhenaten – was determined on a religious revolution. He swept away the pantheon, and replaced it by a proto-monotheistic cult of Aten, represented only as the solar disc. The worship of Aten was carried out in courtyard temples open to the sky, not dark labyrinths. The Pharaoh and queen became the unique intermediaries between the people and Aten, and the priests were out of a job. They did not appreciate this, and after Akhenaten’s death staged a successful counter-revolution. His son Tutankhamun (by another wife) was buried surrounded by images of the old pantheon. The Aten cult was forgotten, the new capital at Amarna abandoned. While it lasted Queen Nefertiti was a sacred priest-empress, as near to a goddess as monotheism allows.

Did the cult die? Sigmund Freud for one thought not. He suggested that the Aten religion influenced Jewish monotheism. Archaeologists pooh-pooh this. The Egyptian captivity is generally considered unhistorical; all the evidence points to a Canaanite origin for Judaism. But in that case, where did the story of the Exodus come from? Canaan was often a frontier province of the Egyptian empire. Metropolitan political and cultural upheavals would have filtered there during Akhenaten’s quite long reign (ca. 1350 BCE) . A contribution to early Jewish developments is certainly possible – it’s more believable than the bloodthirsty fantasies of the unread Book of Joshua. Once you ask “Why not one?” the question is hard to put away.

Maybe Nefertiti is still our Queen.

*     *     *     *     *

PS: If you enjoyed my offbeat art history, you might take a look at some older posts on women subjects and great artists: Bernini, Botticelli, Ghirlandaio, Michelangelo.

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